{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "import sklearn.linear_model\n",
    "import matplotlib\n",
    "\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['figure.figsize'] = (5.0, 4.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MHTOAqWMGBAS0o8dNTV1DSLhl8NTdSShmPFZqtkX4KMnHqVCKCdoeN8Y0iUha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\nrB3eYIu2uMiNMd4NIKspuF9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QkbYi0t7/M3ARsJoUjVEdzhNAROYC5+DNVrIVuA9YAMwH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\nwf8HCbgvFIwK5BwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b81f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "from sklearn import linear_model\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "lr = linear_model.LinearRegression()\n",
    "boston = datasets.load_boston()\n",
    "y = boston.target\n",
    "\n",
    "# cross_val_predict returns an array of the same size as `y` where each entry\n",
    "# is a prediction obtained by cross validation:\n",
    "predicted = cross_val_predict(lr, boston.data, y, cv=10)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(y, predicted)\n",
    "ax.plot([y.min(), y.max()], [y.min(), y.max()], 'k--', lw=4)\n",
    "ax.set_xlabel('Measured')\n",
    "ax.set_ylabel('Predicted')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 2)\n",
      "[[ 24.          30.05313242]\n",
      " [ 21.6         24.73597649]\n",
      " [ 34.7         30.36436055]\n",
      " ..., \n",
      " [ 23.9         28.08877391]\n",
      " [ 22.          26.55246279]\n",
      " [ 11.9         22.64514135]]\n"
     ]
    }
   ],
   "source": [
    "B = np.array([y]).T\n",
    "C = np.array([predicted]).T\n",
    "D = np.hstack((B, C))\n",
    "print(D.shape)\n",
    "print(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DBC1BEqakCK2dwlL4nJaQxd0XTyOaSLJ4Rbtre/gHV3fw5dNPZvTwCPdddio3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\nmDYzIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b7b12b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.axhline(0, linestyle='--', color='black', linewidth=1) # horizontal lines\n",
    "ax.axvline(0, linestyle='--',color='black', linewidth=1)\n",
    "# ax.set_xticks([0])\n",
    "# ax.set_yticks(np.arange(0.1,0.1))\n",
    "plt.scatter(D[:,0], D[:,1],s=20)\n",
    "plt.title(\"Original Data\")\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "D-=np.mean(D, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z4KC1uS8aJxo33PTEBhat2czsqS08ffWpGRFiP7bs7ObCz40iYfLLcwxZwivv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9ea9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.axhline(0, linestyle='--', color='black', linewidth=1) # horizontal lines\n",
    "ax.axvline(0, linestyle='--',color='black', linewidth=1)\n",
    "# ax.set_xticks([0])\n",
    "# ax.set_yticks(np.arange(0.1,0.1))\n",
    "ax.set_xlim([-40,40])\n",
    "ax.set_ylim([-25, 25])\n",
    "plt.scatter(D[:,0], D[:,1], s=20)\n",
    "plt.title(\"Zero Centered data\")\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.15968566  0.96069735]\n",
      " [-0.10152429  0.28445945]\n",
      " [ 1.32424667  1.00027946]\n",
      " ..., \n",
      " [ 0.14880191  0.71086949]\n",
      " [-0.0579893   0.51548086]\n",
      " [-1.15724782  0.01854625]]\n"
     ]
    }
   ],
   "source": [
    "D /= np.std(D, axis = 0)\n",
    "print(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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J4WiF5T5Hy5PD0QrLfY6WJ4ejFZb7HC1PDkczswSHo5lZgsPRzCzB4WhmluBwtMJyn6Pl\nyeFoheU+R8uTw9EKy32Olqc+haOkD0laLqlDUnOXsSslrZa0UtIZfSvTbE/uc7Q89fWvDy4D/hb4\nz/KVkiYDM4HjgXHA/ZKOjYj2Ps5nZlYVfTpyjIgVEbEyMTQDuDkiWiPij8BqYEpf5jIzq6a8XnMc\nD6wtu70uW2dmVgjdnlZLuh84IjE0JyLu6GsBki4CLgI48sgj+7o7M7OK6DYcI+L0/djvemBC2e2m\nbF1q/9cD1wM0NzfHfsxlByj3OVqe8jqtXgjMlNQo6WhgEvBYTnPZAcp9jpanvrbyfEDSOuDtwF2S\n7gGIiOXAAuBJ4JfAxb5SbZXmPkfLkyLq50y2ubk5Wlpaal2GFYQk6un31+qXpEUR0dz9lq/zO2TM\nzBIcjmZmCQ5HM7MEh6OZWYLD0QrLfY6WJ4ejFZb7HC1PDkcrLPc5Wp4cjlZY/jxHy5PD0cwsweFo\nZpbgcDQzS3A4mpklOBytsNznaHlyOFphuc/R8uRwtMJyn6PlyeFoheU+R8uTw9HMLMHhaGaW4HA0\nM0twOJqZJTgcrbDc52h5cjhaYbnP0fLkcLTCcp+j5cnhaIXlPkfLk8PRzCzB4WhmluBwNDNLcDia\nmSU4HK2w3OdoeXI4WmG5z9Hy5HC0wnKfo+XJ4WiF5T5Hy5PD0cwsweFoZpbgcDQzS+hTOEq6VtJT\nkpZKul3S8LKxKyWtlrRS0hl9L9XMrHr6euR4H/CWiDgBeBq4EkDSZGAmcDwwDfiupIY+zmW2G/c5\nWp76FI4RcW9EtGU3HwWasuUZwM0R0RoRfwRWA1P6MpdZV+5ztDxV8jXHC4FfZMvjgbVlY+uydXuQ\ndJGkFkktW7ZsqWA51t+5z9Hy1G04Srpf0rLE14yybeYAbcCNvS0gIq6PiOaIaB49enRv724HMPc5\nWp4GdrdBRJy+r3FJHwOmA6dFRGSr1wMTyjZrytaZmRVCX69WTwMuB86OiFfKhhYCMyU1SjoamAQ8\n1pe5zMyqqdsjx258G2gE7pME8GhEfDoilktaADxJ6XT74oho7+NcZmZV06dwjIhj9jF2NXB1X/Zv\nZlYrfoeMFZb7HC1PDkcrLPc5Wp4cjlZY7nO0PDkcrbDc52h5cjiamSU4HM3MEhyOZmYJDkczswSH\noxWW+xwtTw5HKyz3OVqeHI5WWO5ztDw5HK2w3OdoeXI4mpklOBzNzBIcjmZmCQ5HM7MEvf5nX2pP\n0jZgZa3ryIwCnqt1ERnXkuZa0uqllnqpA+C4iBjamzv09c8kVNrKiGiudREAklpcy55cS5prqd86\noFRLb+/j02ozswSHo5lZQr2F4/W1LqCMa0lzLWmuZU/1UgfsRy11dUHGzKxe1NuRo5lZXXA4mpkl\n1FU4SrpUUkgaVbbuSkmrJa2UdEYVaviKpKWSFku6V9K4GtZyraSnsnpulzS8FrVI+pCk5ZI6JDV3\nGavqc5LNOS2bb7Wk2dWYs2zuH0raLGlZ2brDJd0naVX2fUSVapkg6VeSnsx+Pp+rVT2SDpL0mKQl\nWS1frlUt2bwNkn4n6c79riMi6uILmADcA6wBRmXrJgNLgEbgaOAZoCHnOg4rW/4s8L0a1vJeYGC2\nfA1wTS1qAf4COA54CGguW1+L56Qhm+eNwOBs/slV/D09FTgFWFa27mvA7Gx5dufPqQq1jAVOyZaH\nAk9nP5Oq1wMIGJItDwJ+C7yths/NPwE/Ae7c359RPR05fhO4HCi/QjQDuDkiWiPij8BqYEqeRUTE\nS2U3Dy2rpxa13BsRbdnNR4GmWtQSESsiIvXOpao/J9n+V0fEHyJiJ3BzVkdVRMTDwJ+7rJ4BzM+W\n5wPnVKmWjRHxRLa8DVgBjK9FPVGyPbs5KPuKWtQiqQl4H/D9stW9rqMuwlHSDGB9RCzpMjQeWFt2\ne122Lu96rpa0FvgocFUtaylzIfCLOqmlUy3qqJfHXm5MRGzMlp8FxlS7AEkTgZMpHbHVpJ7sVHYx\nsBm4LyJqVcu/UzrQ6ihb1+s6qvb2QUn3A0ckhuYAX6R0ClnzWiLijoiYA8yRdCVwCZDbHyvprpZs\nmzlAG3BjLeuw7kVESKpqf5ykIcBtwOcj4iVJNaknItqBk7LXxm+X9JYu47nXImk6sDkiFkl6117q\n7FEdVQvHiDg9tV7SX1J6vWpJ9kNtAp6QNAVYT+m1yE5N2bpcakm4EbibUjjWpBZJHwOmA6dF9oJJ\nHrX04jkpl8tzUodzdmeTpLERsVHSWEpHTlUhaRClYLwxIn5W63oAIuIFSb8CptWglqnA2ZLOAg4C\nDpN0w/7UUfPT6oj4fUS8ISImRsRESqdJp0TEs8BCYKakRklHA5OAx/KsR9KkspszgKey5VrUMo3S\n6cHZEfFK2VDVa9mLWtTxODBJ0tGSBgMzszpqaSEwK1ueBVTlSFulo4kfACsi4hu1rEfS6M5uCkkH\nA++h9G+nqrVExJUR0ZRlyUzgwYj4u/2qoxpXjnp5lelPZFers9tzKF2dXAmcWYX5bwOWAUuBnwPj\na1jLakqvry3Ovr5Xi1qAD1D6T6sV2ATcU6vnJJvzLEpXZp+hdNpfzd/Pm4CNwK7sOfkEMBJ4AFgF\n3A8cXqVa3knposfSst+Rs2pRD3AC8LuslmXAVdn6mjw32dzv4vWr1b2uw28fNDNLqPlptZlZPXI4\nmpklOBzNzBIcjmZmCQ5HM7MEh6OZWYLD0cws4f8B3HJSm20FoS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b80c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.axhline(0, linestyle='--', color='black', linewidth=1) # horizontal lines\n",
    "ax.axvline(0, linestyle='--',color='black', linewidth=1)\n",
    "# ax.set_xticks([0])\n",
    "# ax.set_yticks(np.arange(0.1,0.1))\n",
    "ax.set_xlim([-40,40])\n",
    "ax.set_ylim([-25, 25])\n",
    "plt.scatter(D[:,0], D[:,1], s=20)\n",
    "plt.title(\"Normalized data\")\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
